Method and apparatus for determining the second phase of defibrillator devices

ABSTRACT

A method for determining an optimal transchest external defibrillation waveform which, when applied through a plurality of electrodes positioned on a patient&#39;s torso will produce a desired response in the patient&#39;s cardiac cell membranes. The method includes the steps of providing a quantitative model of a defibrillator circuit for producing external defibrillation waveforms, the quantitative model of a patient includes a chest component, a heart component, a cell membrane component and a quantitative description of the desired cardiac membrane response function. Finally, a quantitative description of a transchest external defibrillation waveform that will produce the desired cardiac membrane response function is computed. The computation is made as a function of the desired cardiac membrane response function, the patient model and the defibrillator circuit model.

RELATED APPLICATIONS

This application claims priority to copending non-provisionalapplication Ser. No. 08/886,736, filed Jul. 1, 1997, entitled METHOD ANDAPPARATUS FOR DETERMINING THE SECOND PHASE OF EXTERNAL DEFIBRILLATORDEVICES, which is based on provisional patent application Ser. No.60/021,161, filed Jul. 1, 1996 entitled DYNAMIC SECOND PHASE (φ₂) WITHSELF-CORRECTING CHARGE BURPING FOR EXTERNAL DEFIBRILLATOR DEVICES, thecontents of both applications of which are herein incorporated byreference.

FIELD OF THE INVENTION

This invention relates generally to an electrotherapy method andapparatus for delivering an electrical pulse to a patient's heart. Inparticular, this invention relates to a method and apparatus fortailoring a second phase of biphasic waveform delivered by an externaldefibrillator, to random patients, by performing intelligentcalculations and analysis to the results of a first phase segment of abiphasic defibrillation waveform and other parameters pertaining theretobased on theory and practice as disclosed herein.

BACKGROUND OF THE INVENTION

Devices for defibrillating a heart have been known for sometime now.Implantable defibrillators are well accepted by the medical community aseffective tools to combat fibrillation for an identified segment of thepopulation. A substantial amount of research in fibrillation and thetherapy of defibrillation has been done. Much of the most recentresearch has concentrated on understanding the effects that adefibrillation shock pulse has on fibrillation to terminate such acondition.

A monophasic waveform is defined to be a single phase,capacitive-discharge, time-truncated, waveform with exponential decay. Abiphasic waveform is defined to comprise two monophasic waveforms,separated by time and of opposite polarity. The first phase isdesignated φ₁ and the second phase is designated φ₂. The delivery of φ₁is completed before the delivery of φ₂ is begun.

After extensive testing, it has been determined that biphasic waveformsare more efficacious than monophasic waveforms. There is a wide debateregarding the reasons for the increased efficacy of biphasic waveformsover that of a monophasic waveforms. One hypothesis holds that φ₁defibrillates the heart and φ₂ performs a stabilizing action that keepsthe heart from refibrillating.

Biphasic defibrillation waveforms are now the standard of care inclinical use for defibrillation with implantablecardioverter-defibrillators (ICDs), due to the superior performancedemonstrated over that of comparable monophasic waveforms. To betterunderstand these significantly different outcomes, ICD research hasdeveloped cardiac cell response models to defibrillation. Waveformdesign criteria have been derived from these first principles and havebeen applied to monophasic and biphasic waveforms to optimize theirparameters. These principles-based design criteria have producedsignificant improvements over the current art of waveforms.

In a two paper set, Blair developed a model for the optimal design of amonophasic waveform when used for electrical stimulation. (1) Blair, H.A., “On the Intensity-time relations for stimulation by electriccurrents.” I. J. Gen. Physiol. 1932; 15: 709-729. (2) Blair, H. A., “Onthe Intensity-time Relations for stimulation by electric currents. II.J. Gen. Physiol. 1932; 15: 731-755. Blair proposed and demonstrated thatthe optimal duration of a monophasic waveform is equal to the point intime at which the cell response to the stimulus is maximal. DuplicatingBlair's model, Walcott extended Blair's analysis to defibrillation,where they obtained supporting experimental results. Walcott, et al.,“Choosing the optimal monophasic and biphasic waveforms for ventriculardefibrillation.” J. Cardiovasc Electrophysiol. 1995; 6: 737-750.

Independently, Kroll developed a biphasic model for the optimal designof φ₂ for a biphasic defibrillation waveform. Kroll, M. W., “A minimalmodel of the single capacitor biphasic defibrillation waveform.” PACE1994; 17: 1782-1792. Kroll proposed that the φ₂ stabilizing actionremoved the charge deposited by φ₁ from those cells not stimulated byφ₁. This has come to be known as “charge burping”. Kroll supported hishypothesis with retrospective analysis of studies by Dixon, et al.,Tang, et al., and Freese, et al. regarding single capacitor, biphasicwaveform studies. Dixon, et al., “Improved defibrillation thresholdswith large contoured epicardial electrodes and biphasic waveforms.”Circulation 1987; 76: 1176-1184; Tang, et al. “Ventriculardefibrillation using biphasic waveforms: The Importance of Phasicduration.” J. Am. Coll. Cardiol. 1989; 13: 207-214; and Feeser, S. A.,et al. “Strength-duration and probability of success curves fordefibrillation with biphasic waveforms.” Circulation 1990; 82:2128-2141. Again, the Walcott group retrospectively evaluated theirextension of Blair's model to φ₂ using the Tang and Feeser data sets.Their finding further supported Kroll's hypothesis regarding biphasicdefibrillation waveforms. For further discussions on the development ofthese models, reference may be made to PCT publications WO 95/32020 andWO 95/09673 and to U.S. Pat. No. 5,431,686.

The charge burping hypothesis can be used to develop equations thatdescribe the time course of a cell's membrane potential during abiphasic shock pulse. At the end of φ₁, those cells that were notstimulated by φ₁ have a residual charge due to the action of φ₁ on thecell. The charge burping model hypothesizes that an optimal pulseduration for φ₂ is that duration that removes as much of the φ₁ residualcharge from the cell as possible. Ideally, these unstimulated cells areset back to “relative ground.” The charge burping model proposed byKroll is based on the circuit model shown in FIG. 2b which is adaptedfrom the general model of a defibrillator illustrated in FIG. 2a.

The charge burping model also accounts for removing the residual cellmembrane potential at the end of a φ₁ pulse that is independent of a φ₂.That is, φ₂ is delivered by a set of capacitors separate from the set ofcapacitors used to deliver φ₁. This charge burping model is constructedby adding a second set of capacitors, as illustrated in FIG. 3. In thisfigure, C₁ represents the φ₁ capacitor set, C₂ represents the φ₂capacitor set R_(H) represents the resistance of the heart, and the pairC_(M) and R_(M) represent membrane series capacitance and resistance ofa single cell. The node V_(S) represents the voltage between theelectrodes, while V_(M) denotes the voltage across the cell membrane.

External defibrillators send electrical pulses to the patient's heartthrough electrodes applied to the patient's torso. Externaldefibrillators are useful in any situation where there may be anunanticipated need to provide electrotherapy to a patient on shortnotice. The advantage of external defibrillators is that they may beused on a patient as needed, then subsequently moved to be used withanother patient.

However, this important advantage has two fundamental limitations.First, external defibrillators do not have direct contact with thepatient's heart. External defibrillators have traditionally deliveredtheir electrotherapeutic pulses to the patient's heart from the surfaceof the patient's chest. This is known as the transthoracicdefibrillation problem. Second, external defibrillators must be able tobe used on patients having a variety of physiological differences.External defibrillators have traditionally operated according to pulseamplitude and duration parameters that can be effective in all patients.This is known as the patient variability problem.

The prior art described above effectively models implantabledefibrillators, however it does not fully addressed the transthoracicdefibrillation problem nor the patient variability problem. In fact,these two limitations to external defibrillators are not fullyappreciated by those in the art. For example, prior art disclosures ofthe use of truncated exponential monophasic or biphasic shock pulses inimplantable or external defibrillators have provided little guidance forthe design of an external defibrillator that will successfullydefibrillate across a large, heterogeneous population of patients. Inparticular, an implantable defibrillator and an external defibrillatorcan deliver a shock pulse of similar form, and yet the actualimplementation of the waveform delivery system is radically different.

In the past five years, new research in ICD therapy has developed anddemonstrated defibrillation models that provide waveform design rulesfrom first principles. These defibrillation models and their associateddesign rules for the development of defibrillation waveforms and theircharacteristics were first developed by Kroll and Irnich for monophasicwaveforms using effective and rheobase current concepts. (1) Kroll, M.W., “A minimal model of the monophasic defibrillation pulse.” PACE 1993;15: 769. (2) Irnich, W., “Optimal truncation of defibrillation pulses.”PACE 1995; 18: 673. Subsequently, Kroll, Walcott, Cleland and othersdeveloped the passive cardiac cell membrane response model formonophasic and biphasic waveforms, herein called the cell responsemodel. (1) Kroll, M. W., “A minimal model of the single capacitorbiphasic defibrillation waveform.” PACE 1994; 17: 1782. (2) Walcott, G.P., Walker, R. G., Cates. A. W., Krassowska, W., Smith, W. M, Ideker RE. “Choosing the optimal monophasic and biphasic waveforms forventricular defibrillation.” J Cardiovasc Electrophysiol 1995; 6: 737;and Cleland B G. “A conceptual basis for defibrillation waveforms.” PACE1996; 19: 1186).

A significant increase in the understanding of waveform design hasoccurred and substantial improvements have been made by using thesenewly developed design principles. Block et al. has recently written acomprehensive survey of the new principles-based theories and theirimpact on optimizing internal defibrillation through improved waveforms.Block M, Breithardt G., “Optimizing defibrillation through improvedwaveforms.” PACE 1995; 18: 526.

There have not been significant developments in external defibrillationwaveforms beyond the two basic monophasic waveforms: the damped sine orthe truncated exponential. To date, their design for transthoracicdefibrillation has been based almost entirely on empirically deriveddata. It seems that the design of monophasic and biphasic waveforms forexternal defibrillation has not yet been generally influenced by theimportant developments in ICD research.

Recently there has been reported research on the development andvalidation of a biphasic truncated exponential waveform in which it wascompared clinically to a damped sine waveform. For additionalbackground, reference may be made to U.S. Pat. Nos. 5,593,427, 5,601,612and 5,607,454. See also: Gliner B E, Lyster T E, Dillon S M, Bardy G H,“Transthoracic defibrillation of swine with monophasic and biphasicwaveforms.” Circulation 1995; 92: 1634-1643; Bardy G H, Gliner B E,Kudenchuk P J, Poole J E, Dolack G L, Jones G K, Anderson J, Troutman C,Johnson G.; “Truncated biphasic pulses for transthoracicdefibrillation.” Circulation 1995; 91: 1768-1774; and Bardy G H et al,“For the Transthoracic Investigators. Multicenter comparison oftruncated biphasic shocks and standard damped sine wave monophasicshocks for transthoracic ventricular defibrillation.” Circulation 1996;94: 2507-2514. Although the research determined a usable biphasicwaveform, there was no new theoretical understanding determined forexternal waveform design. It appears that external waveform research maydevelop a “rules-of-thumb by trial and error” design approach much likethat established in the early stages of theoretical ICD research. Thenoted limitations of the transthoracic biphasic waveform may be due inpart to a lack of principles-based design rules to determine itswaveform characteristics.

There is a continued need for a device designed to perform a quick andautomatic adjustment of phase 2 relative to phase 1 if AED's are to beadvantageously applied to random patients according to a cell responsemodel. Further, the model and the device must be adaptable to patientvariance and be able to provide automatic adjustment in a dynamicenvironment.

SUMMARY OF THE INVENTION

The present invention relates to an external defibrillation method andapparatus that addresses the limitations in the prior art. The presentinvention incorporates three singular practices that distinguish thepractice of designing external defibrillators from the practice ofdesigning implantable defibrillators. These practices are 1) designingmultiphasic transthoracic shock pulse waveforms from principles based oncardiac electrophysiology, 2) designing multiphasic transthoracic shockpulse waveforms in which each phase of the waveform can be designedwithout implementation limitations placed on its charging and deliverymeans by such means for prior waveform phases, and 3) designingmultiphasic transthoracic shock pulse waveforms to operate across a widerange of parameters determined by a large, heterogeneous population ofpatients.

In particular, the present invention provides for a method and apparatusfor tailoring and reforming a second phase (φ₂) of a biphasicdefibrillation waveform relative to a first phase (φ₁) of the waveformbased on intelligent calculations. The method includes the steps ofdetermining and providing a quantitative description of the desiredcardiac membrane response function. A quantitative model of adefibrillator circuit for producing external defibrillation waveforms isthen provided. Also provided is a quantitative model of a patient whichincludes a chest component, a heart component and a cell membranecomponent. A quantitative description of a transchest externaldefibrillation waveform that will produce the desired cardiac membraneresponse function is then computed. Intelligent calculations based onthe phase 1 cell response is then computed to determine the desiredphase 2 waveform. The computation is made as a function of the desiredcardiac membrane response function, the patient model and thedefibrillator circuit model.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1a and 1 b are perspective views of an AED according to thepresent invention.

FIG. 2a is a very simplified defibrillator model.

FIG. 2b is a known monophasic defibrillation model.

FIG. 3 is a known biphasic defibrillation model.

FIG. 4 represents a monophasic or biphasic capacitive-discharge externaldefibrillation model according to the present invention.

FIG. 5a represents a monophasic capacitor-inductor externaldefibrillator model according to the present invention.

FIG. 5b represents an alternative embodiment of a biphasiccapacitor-inductor external defibrillator model according to the presentinvention.

FIG. 6 illustrates a biphasic waveform generator utilizing the presentinvention.

FIG. 7 is a schematic diagram of a circuit which enables theimplementation of the present invention.

FIG. 8 illustrates a biphasic waveform in relation to a cellularresponse curve.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention provides a method and apparatus for tailoring asecond phase (φ₂) of a biphasic waveform delivered by an externaldefibrillator, to random patients, by performing intelligentcalculations and analysis to the results of a first phase (φ₁) segmentof a biphasic defibrillation waveform and other parameters pertainingthereto. Prior to describing the present invention, a discussion of thedevelopment of an external defibrillation model will be given.

External Defibrillator Model

The apparatus of the present invention is an automated externaldefibrillator (AED) illustrated in FIGS. 1a and 1 b. FIG. 1a illustratesan AED 10, including a plastic case 12 with a carrying handle 14. A lid16 is provided which covers an electrode compartment 18. An electrodeconnector 20, a speaker 22 and a diagnostic panel (not shown) arelocated on case 12 within electrode compartment 18. FIG. 1b illustratesAED 10 having a pair of electrodes 24 connected thereto. Electrodes 24can be pre-connected to connector 20 and stored in compartment 18.

The operation of AED 10 is described briefly below. A rescue mode of AED10 is initiated when lid 16 is opened to access electrodes 24. Theopening of lid 16 is detected by AED 10 to effectively turn on thedevice. AED 10 then quickly runs a short test routine. After electrodes24 have been placed on the patient, AED 10 senses patient specificparameters, such as impedance, voltage, current, charge or othermeasurable parameters of the patient. The patient specific parametersare then utilized in the design of optimal waveforms as will bedescribed below.

If a shockable condition is detected through electrodes 24, a pluralityof capacitors inside of AED 10 are charged from an energy source,typically a detachable battery pack. Based upon the patient specificparameters sensed, the duration and other characteristics of a dischargewaveform are then calculated. The energy stored in AED 10 is thendischarged to the patient through electrodes 24.

For a more detailed description of the physical structure of AED 10 orthe process involved in sensing, charging, shocking and testing,reference should be made to applicants co-pending application Ser. No.08/512,441, filed Aug. 8, 1995 entitled AUTOMATED EXTERNAL DEFIBRILLATORWITH SELF-TEST SYSTEM which is assigned to the assignee of the presentinvention, the disclosure of which is herein incorporated by reference.

In the present invention it is not assumed that both phases of abiphasic waveform are delivered using the same set of capacitors or thatboth phases of a biphasic waveform are delivered using the capacitor setin the same electrical configuration, although such an embodiment isconsidered within the spirit and scope of the present invention.

Transthoracic defibrillation is generally performed by placingelectrodes on the apex and anterior positions of the chest wall. Withthis electrode arrangement, nearly all current passing through the heartis conducted by the lungs and the equipotential surfaces pass throughthe myocardium normal to the electrode axis. The present invention usesthe transthoracic charge burping model to develop design equations thatdescribe the time course of a cell's membrane potential during atransthoracic biphasic shock pulse. These equations are then used tocreate equations that describe the design of monophasic and biphasicshock pulses for transchest defibrillation to optimize the design of φ₁for defibrillating and the design φ₂ for stabilizing. These optimizingshock pulse design equations are called design rules.

According to the present invention, the main series pathway for currentis to pass through the chest wall, the lungs, and the heart.Additionally, there are two important shunting pathways in parallel withthe current pathway through the heart. These shunting pathways must betaken into consideration. The lungs shunt current around the heartthrough a parallel pathway. The second shunting pathway is provided bythe thoracic cage. The resistivity of the thoracic cage and the skeletalmuscle structure is low when compared to lungs. The high resistivity ofthe lungs and the shunting pathways are characterizing elements ofexternal defibrillation that distinguish the art from intracardiacdefibrillation and implantable defibrillation technologies.

Therefore, in the transthoracic defibrillation model of the presentinvention illustrated in FIG. 4, there are several resistances inaddition to those discussed for the charge burping model above. R_(S)represents the resistance of the defibrillation system, including theresistance of the defibrillation electrodes. R_(CW) and R_(LS) representthe resistances of the chest wall and the lungs, respectively, in serieswith resistance of the heart, R_(H). R_(TC) and R_(LP) represent theresistances of the thoracic cage and the lungs, respectively, inparallel with the resistance of the heart.

The design rules for external defibrillation waveforms are determined inthree steps. In the first step, the transchest forcing function isdetermined. The transchest forcing function is the name that is given tothe voltage that is applied across each cardiac cell during an externaldefibrillation shock. In the second step, the design equations for φ₁ ofa shock pulse are determined. The design equations are the equationsdescribing the cell's response to the φ₁ transchest forcing function,the equation describing the optimal φ₁ pulse duration, and the equationdescribing the optimal φ₁ capacitor. Therefore, step two relates thecell response to the action of a monophasic shock pulse or the firstphase of a biphasic shock pulse. This relation is used to determine theoptimal design rules and thereby design parameters for theimplementation of this phase in an external defibrillator. It will beclear to those in the art that step two is not restricted to capacitordischarge shock pulses and their associated transchest forcing function.Another common implementation of an external defibrillator incorporatesa damped sine wave for a shock pulse and can be either a monophasic orbiphasic waveform. This type of external defibrillator is modeled by thecircuits shown in FIGS. 5a and 5 b. In the third step, the designequations for φ₂ of a shock pulse are determined. The design equationsare the equations describing the cell's response to the φ₂ transchestforcing function, the equation describing the optimal φ₂ pulse durationand the equation describing the optimal φ₂ capacitor. These designequations are employed to determine the optimal design rules and therebydesign parameters of φ₂ of a biphasic shock pulse with respect to howthe cell responds to the shock pulse. An important element of thisinvention is to provide shock pulse waveforms that are designed from acardiac cell response model developed from first principles and thatcorrectly determines the effects of the chest and its components on theability of a shock pulse to defibrillate.

The transchest forcing function is determined by solving for the voltagefound at node V₃ in FIG. 4. The transchest forcing function is derivedby solving for V₃ using the following three nodal equations:$\begin{matrix}{{{\frac{V_{1} - V_{S}}{R_{S}} + \frac{V_{1}}{R_{TC}} + \frac{V_{1} - V_{2}}{R_{CW}}} = 0},} & (1) \\{{{\frac{V_{2} - V_{1}}{R_{CW}} + \frac{V_{2}}{R_{LP}} + \frac{V_{2} - V_{3}}{R_{LS}}} = 0},{and}} & (2) \\{{\frac{V_{3} - V_{2}}{R_{LS}} + \frac{V_{3}}{R_{H}} + \frac{V_{3} - V_{M}}{R_{M}}} = 0.} & (3)\end{matrix}$

Equation 1 can be rewritten as $\begin{matrix}{{V_{1}\left( {\frac{1}{R_{S}} + \frac{1}{R_{BC}} + \frac{1}{R_{CW}}} \right)} = {\frac{V_{S}}{R_{S}} + {\frac{V_{2}}{R_{CW}}.}}} & \text{(4A)} \\{{{V_{1} = {\frac{V_{S}}{R_{S}\Omega_{1}} + \frac{V_{2}}{R_{CW}\Omega_{1}}}},{where}}{\Omega_{1} = {\frac{1}{R_{S}} + \frac{1}{R_{{TC}\quad}} + {\frac{1}{R_{CW}}.}}}} & \text{(4B)}\end{matrix}$

Rewriting equation 2, we have $\begin{matrix}{{V_{2}\left( {\frac{1}{R_{CW}} + \frac{1}{R_{LP}} + \frac{1}{R_{LS}}} \right)} = {\frac{V_{1}}{R_{CW}} + {\frac{V_{3}}{R_{LS}}.}}} & \text{(4C)}\end{matrix}$

By substituting equation 4B for V₁ into equation 4C, we can solve for V₂as an expression of V_(S) and V₃: $\begin{matrix}{{{V_{2} = {\frac{V_{S}}{R_{S}R_{CW}\Omega_{1}\Omega_{2}\Omega_{22}} + \frac{V_{3}}{R_{LS}\Omega_{2}\Omega_{22}}}},{where}}{{\Omega_{2} = {\frac{1}{R_{LS}} + \frac{1}{R_{LP}} + \frac{1}{R_{CW}}}},{and}}{\Omega_{22} = {1 - {\frac{1}{R_{CW}^{2}\Omega_{1}\Omega_{2}}.}}}} & (5)\end{matrix}$

Now solving for V₃ as an expression of V_(S) and V_(M), equation 3 maybe re-arranged as $\begin{matrix}{{{V_{3}\left( {\frac{1}{R_{LS}} + \frac{1}{R_{H}} + \frac{1}{R_{M}}} \right)} = {\frac{V_{2}}{R_{LS}} + \frac{V_{M}}{R_{M}}}}{{so}\quad {that}}} & (6) \\{{V_{3} = {\frac{V_{2}}{R_{LS}\Omega_{3}} + \frac{V_{M}}{R_{M}\Omega_{3}}}}{{{where}\quad \Omega_{3}} = {\frac{1}{R_{LS}} + \frac{1}{R_{H}} + {\frac{1}{R_{M}}.}}}} & (7)\end{matrix}$

Substituting equation 5 for V₂ into equation 7, we can solve for V₃ asan expression of V_(S) and V_(M): $\begin{matrix}{{V_{3} = {\frac{V_{S}}{R_{S}R_{CW}R_{LS}\Omega_{1}\Omega_{2}\Omega_{22}\Omega_{3}\Omega_{33}} + \frac{V_{M}}{R_{M}\Omega_{3}\Omega_{33}}}}{where}} & (8) \\{\Omega_{33} = {1 - \frac{1}{\left( {R_{LS}^{2}\Omega_{2}\Omega_{22}\Omega_{3}} \right)}}} & (9)\end{matrix}$

From equation 8 we define Ω_(M) to be: $\begin{matrix}{{\Omega_{M} = {{R_{M}\Omega_{3}\Omega_{33}} = {R_{M}{\Omega_{3}\left( {1 - \frac{1}{\left( {R_{LS}^{2}\Omega_{2}\Omega_{22}\Omega_{3}} \right)}} \right)}}}}{\Omega_{M} = {{R_{M}\left( {\Omega_{3} - \frac{1}{R_{LS}^{2}\left( {\Omega_{2} - \frac{1}{R_{CW}^{2}\Omega_{1}}} \right)}} \right)}.}}} & (10)\end{matrix}$

From equation 8 we also define Ω_(S) to be:

Ω_(S) =R _(S) R _(CW) R _(LS)Ω₁Ω₂Ω₃Ω₂₂Ω₃₃  (11)

$\begin{matrix}{\Omega_{S} = {R_{S}R_{CW}R_{LS}\Omega_{1}{\Omega_{2}\left( {1 - \frac{1}{\left( {R_{CW}^{2}\Omega_{1}\Omega_{2}} \right)}} \right)}{\Omega_{3}\left( {1 - \frac{1}{\left( {R_{LS}^{2}\Omega_{2}\Omega_{22}\Omega_{3}} \right)}} \right)}}} & (12) \\{\Omega_{S} = {R_{S}R_{CW}{R_{LS}\left( {{\Omega_{1}\Omega_{2}} - \frac{1}{R_{CW}^{2}}} \right)}\left( {\Omega_{3} - \frac{1}{R_{LS}^{2}\left( {\Omega_{2} - \frac{1}{R_{CW}^{2}\Omega_{1}}} \right)}} \right)}} & (13) \\{{{so}\quad {that}\quad V_{3}} = {\frac{V_{S}}{\Omega_{S}} + \frac{V_{M}}{\Omega_{M}}}} & (14)\end{matrix}$

is the general transchest transfer function as shown in FIG. 4 or FIGS.5a and 5 b. Equation 14 encapsulates the transchest elements and theirassociation between the forcing function V_(S) (which models adefibrillation circuit and the shock pulse) and the cell membranevoltage V_(M). Therefore, this completes the first step.

The variable V_(S) may now be replaced with a more specific descriptionof the defibrillation circuitry that implements a shock pulse. For afirst example, a monophasic time-truncated, capacitive-discharge circuitmay be represented by V_(S)=V₁e^(-t/τ) ₁, where V₁ is the leading-edgevoltage for the shock pulse and τ₁=RC₁, with R determined below.

As shown in FIGS. 5a and 5 b, a second example would be a monophasicdamped sine wave circuit, represented by $\begin{matrix}{V_{S} = {{V_{1}\left( \frac{\tau_{C1}}{\tau_{C1} - \tau_{L1}} \right)}\left( {^{{- t}/\tau_{C1}} - ^{{- t}/\tau_{L1}}} \right)}} & \text{(14B)}\end{matrix}$

where V₁ is the voltage on the charged capacitor C₁τ_(C1)=RC₁ andτ_(L1)=L₁/R. Every step illustrated below may be performed with this andother similar transchest forcing functions which represent defibrillatorcircuitry.

To proceed with step two, from FIG. 4, nodal analysis provides anequation for V_(M): $\begin{matrix}{{{C_{M}\frac{V_{M}}{t}} + \frac{V_{M} - V_{3}}{R_{M}}} = 0.} & (15)\end{matrix}$

Rearranging equation 15, we have $\begin{matrix}{{{C_{M}\frac{V_{M}}{t}} + \frac{V_{M}}{R_{M}}} = {\frac{V_{3}}{R_{M}}.}} & (16)\end{matrix}$

Next, substituting equation 14 as an expression for V₃ into equation 16,the cell membrane response is now calculated as follows: $\begin{matrix}{{{C_{M}\frac{V_{M}}{t}} + \frac{V_{M}}{R_{M}}} = {\frac{1}{R_{M}}\left( {\frac{V_{S}}{\Omega_{S}} + \frac{V_{M}}{\Omega_{M}}} \right)}} & (17) \\{{{{C_{M}\frac{V_{M}}{t}} + \frac{V_{M}}{R_{M}} - \frac{V_{M}}{R_{M}\Omega_{M}}} = \frac{V_{S}}{R_{M}\Omega_{S}}}{{{C_{M}\frac{V_{M}}{t}} + {\frac{V_{M}}{R_{M}}\left( {1 - \frac{1}{\Omega_{M}}} \right)}} = \frac{V_{S}}{R_{M}\Omega_{S}}}} & (18)\end{matrix}$

Dividing through by C_(M), and setting τ_(M)=R_(M)C_(M), then equation18 becomes $\begin{matrix}{{\frac{V_{M}}{t} + {\frac{V_{M}}{\tau_{M}}\left( {1 - \frac{1}{\Omega_{M}}} \right)}} = {\frac{V_{S}}{\tau_{M}}{\left( \frac{1}{\Omega_{S}} \right).}}} & (19)\end{matrix}$

Equation 19 is a general ordinary differential equation (ODE) thatmodels the effects of any general forcing function V_(S) that representsa phase of a shock pulse waveform applied across the chest. The generalODE equation 19 models the effects of a general shock pulse phase V_(S)on the myocardium, determining cardiac cell response to such a shockpulse phase.

In the equations given below:

C₁ equals the capacitance of the first capacitor bank andV_(S)=V₁e^(-t/τ) ^(₁) ;

C₂ equals the capacitance of the second capacitor bank andV_(S)=V₂e^(-t/τ) ^(₂) ;

R=R_(S)+R_(B), where R_(S)=System impedance (device and electrodes);

R_(B)=body impedance (thoracic cage, chest wall, lungs (series,parallel), heart).

To determine body impedance, R_(B), we see that the series combinationof R_(H) and R_(LS) yields R_(H)+R_(LS). (FIG. 4). The parallelcombination of R_(H)+R_(LS) and R_(LP) yields: $\begin{matrix}{\frac{R_{LP}\left( {R_{LS} + R_{H}} \right)}{R_{LP} + R_{LS} + R_{H}}.} & (20)\end{matrix}$

The series combination of equation 20 and R_(CW) yields: $\begin{matrix}{R_{CW} + {\frac{R_{LP}\left( {R_{LS} + R_{H}} \right)}{\left( {R_{LP} + R_{LS} + R_{H}} \right)}.}} & (21)\end{matrix}$

The parallel combination of equation 21 and R_(TC) yields:$\begin{matrix}{R_{B} = \left\lbrack \frac{R_{TC}\left\lbrack {R_{CW} + \frac{R_{LP}\left( {R_{LS} + R_{H}} \right)}{\left( {R_{LP} + R_{LS} + R_{H}} \right)}} \right.}{R_{TC} + R_{CW} + \frac{R_{LP}\left( {R_{LS} + R_{H}} \right)}{\left( {R_{LP} + R_{LS} + R_{H}} \right)}} \right\rbrack} & (22)\end{matrix}$

where R_(B) is the impedance of the body for this model.

The discharge of a single capacitor is modeled by V_(S)=V₁e^(-t/τ) ^(₁)for an initial C₁ capacitor voltage of V₁. Placing V_(S) into equation19 gives: $\begin{matrix}{{\frac{V_{M}}{t} + {\frac{V_{M}}{\tau_{M}}\left( {1 - \frac{1}{\Omega_{M}}} \right)}} = \frac{V_{1}^{{- t}/\tau_{1}}}{\tau_{M}\Omega_{S}}} & (23)\end{matrix}$

where τ_(M)=R_(M)C_(M) represents the time constant of the myocardialcell in the circuit model, and τ₁, which equals R_(S)C₁, represents thetime constant of φ₁. Such a standard linear ODE as equation 23 has theform ${\frac{y}{x} + {{P(X)}Y}} = {{Q(x)}.}$

These linear ODEs have an integration factor that equals e^(∫pdx). Thegeneral solution to such equations is:

Y=e ^(-∫pdx) [∫e ^(∫pdx) Qdx+c].

The ODE in equation 23 models the effects of each phase of atime-truncated, capacitor-discharged shock pulse waveform. Equation 23is a first-order linear ODE, and may be solved using the method ofintegration factors, to get: $\begin{matrix}{{V_{M1}(t)} = {{k\quad ^{{- {({t/\tau_{M}})}}\quad {({1 - \frac{1}{\Omega_{M}}})}}} + {\left( \frac{V_{1}}{\Omega_{S}} \right)\quad \left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{2}{\Omega_{M}}} \right)} - \tau_{M}} \right){^{{- t}/\tau_{1}}.}}}} & (24)\end{matrix}$

Equation 24 is an expression of cell membrane potential during φ₁ of ashock pulse. To determine the constant of integration k, the initialvalue of V_(M1) is assumed to be V_(M1)(0)=V_(G) (“cell ground”).Applying this initial condition to equation 24, k is found to be$\begin{matrix}{k = {V_{G} - {\left( \frac{V_{o}}{\Omega_{S}} \right)\quad {\left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right).}}}} & (25)\end{matrix}$

Assuming τ₁=R_(C1), where R=R_(S)+R_(B), then the solution to theinitial-value problem for φ₁ is: $\begin{matrix}{{V_{M1}(t)} = {{V_{G}^{{- {({t/\tau_{M}})}}\quad {({1 - \frac{1}{\Omega_{M}}})}}} + {\left( \frac{V_{1}}{\Omega_{S}\quad} \right)\quad \left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right)\left( {^{{- t}/\tau_{1}} - ^{{- {({t/\tau_{M}})}}\quad {({1 - \frac{1}{\Omega_{M}}})}}} \right)}}} & (26)\end{matrix}$

Equation 26 describes the residual voltage found on a cell at the end ofφ₁.

Assuming V_(G)=0 and V₁=1, the solution for cell response to an externalshock pulse is $\begin{matrix}{{V_{M1}(t)} = {\left( \frac{1}{\Omega_{S}} \right)\quad \left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right){\left( {^{- \frac{t}{\tau_{1}}} - ^{{- {(\frac{t}{\tau_{M}})}}{({1 - \frac{1}{\Omega_{M}}})}}} \right).}}} & (27)\end{matrix}$

We may now determine optimal durations for φ₁ according to criteria fordesired cell response. One such design role or criterion is that the φ₁duration is equal to the time required for the external defibrillatorshock pulse to bring the cell response to its maximum possible level. Todetermine this duration, equation 27 is differentiated and the resultingequation 27B is set to zero. Equation 27B is then solved for the time t,which represents shock pulse duration required to maximize cardiac cellresponse. $\begin{matrix}{{{{{\left( \frac{AB}{\tau_{M}} \right)^{{- {Bt}}/\tau_{M}}} - {\left( \frac{A}{\tau_{1}} \right)^{{- t}/\tau_{1}}}} = 0},{{{where}\quad A} = {\left( \frac{1}{\Omega_{S}} \right)\quad \left( \frac{\tau_{1}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right)}}}{{{and}\quad B} = {1 - {\frac{1}{\Omega_{M}}.}}}} & \text{(27B)}\end{matrix}$

Solving for t, the optimal duration dφ₁ for a monophasic shock pulse orφ₁ of a biphasic shock pulse is found to be $\begin{matrix}{{{d\quad \varphi_{1}} = {\left( \frac{\tau_{1}\tau_{M}}{{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right)\quad {\ln\left( \frac{\tau_{1}\left( {1 - \frac{1}{\Omega_{M}}} \right)}{\tau_{M}} \right)}}},} & \text{(27C)}\end{matrix}$

where “1n” represents the logarithm to the base e, the naturallogarithm.

For φ₂, an analysis almost identical to equations 20 through 27 above isderived. The differences are two-fold. First, a biphasic waveformreverses the flow of current through the myocardium during φ₂. Reversingthe flow of current in the circuit model changes the sign on thecurrent. The sign changes on the right hand side of equation 23.

The second difference is the step taken to incorporate an independent φ₂into the charge burping model. Therefore, the φ₂ ODE incorporates the C₂capacitor set and their associated leading-edge voltage, V₂, for the φ₂portion of the pulse. Then τ₂ represents the φ₂ time constant; τ₂=RC₂,and V_(S)=−V₂e^(-t/τ) ^(₂) . Equation 23 now becomes: $\begin{matrix}{{\frac{V_{M}}{t} + {\left( \frac{V_{M}}{\tau_{M}} \right)\quad \left( {1 - \frac{1}{\Omega_{M}}} \right)}} = {\frac{{- V_{2}}^{{- t}/\tau_{2}}}{\tau_{M}\Omega_{S}}.}} & (29)\end{matrix}$

Equation 29 is again a first-order linear ODE. In a similar manner, itsgeneral solution is determined to be: $\begin{matrix}{{V_{M2}(t)} = {{k\quad ^{{({{- t}/\tau_{M}})}\quad {({1 - \frac{1}{\Omega_{M}}})}}} - {\left( \frac{V_{2}}{\Omega_{S}} \right)\quad {\left( \frac{\tau_{2}}{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right).}}}} & (30)\end{matrix}$

To determine the constant of integration k, the value of V_(M2) at theend of φ₁ is

V _(M2)(0)=V _(M1)(d _(φ1))=V _(φ1′)  (31)

where d_(φ1) is the overall time of discharge for φ₁ and V_(φ1) is thevoltage left on the cell at the end of φ₁. Applying the initialcondition to equation 30 and solving for k: $\begin{matrix}{k = {V_{\varphi \quad 1} + {\left( \frac{V_{2}}{\Omega_{S}} \right)\quad {\left( \frac{\tau_{2}}{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right).}}}} & (32)\end{matrix}$

The solution to the initial-value problem for φ₂ is $\begin{matrix}{{V_{M2}(t)} = {{\left( \frac{V_{2}}{\Omega_{S}} \right)\quad \left( \frac{\tau_{2}}{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right)\quad \left( {^{{- {({t/\tau_{M}})}}\quad {({1 - \frac{1}{\Omega_{M}}})}} - ^{{- t}/\tau_{2}}} \right)} + {V_{\varphi \quad 1}{^{{- {({t/\tau_{M}})}}\quad {({1 - \frac{1}{\Omega_{M}}})}}.}}}} & (33)\end{matrix}$

Equation 33 provides a means to calculate the residual membranepotential at the end of φ₂ for the cells that were not stimulated by φ₁.Setting Equation 33 equal to zero, we solve for t, thereby determiningthe duration of φ₂, denoted dφ₂, such that V_(M2)(dφ₂)=0. By designingφ₂ with a duration dφ₂, the biphasic shock pulse removes the residualchange placed on a cell by φ₁. We determine dφ₂ to be: $\begin{matrix}{d_{\varphi 2} = {{\left( \frac{\tau_{2}\tau_{M}}{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}} \right) \cdot \ln}\quad {\left( {1 + {\left( \frac{{\tau_{2}\left( {1 - \frac{1}{\Omega_{M}}} \right)} - \tau_{M}}{\tau_{2}} \right)\left( \frac{\Omega_{S}V_{\varphi \quad 1}}{V_{2}} \right)}} \right).}}} & (34)\end{matrix}$

From the equations above, an optimal monophasic or biphasicdefibrillation waveform may be calculated for an external defibrillator.

As an example, an external defibrillator may be designed as set forthbelow. Assume a monophasic truncated exponential shock pulse, a 200 μFcapacitor, so that τ₁=R·(200 μF). Suppose also that the externaldefibrillator is designed to apply the maximal cardiac cell responsedesign rule (equation 27C) to determine the duration of the discharge.Suppose further that the human cardiac cell time constant is estimatedto be 3±1 ms. Further assume that the external defibrillator energysource comprises five 1000 μF capacitors in series to implement a 200 μFcapacitor bank. If each capacitor is charged to 400V, for a total of2000V for the leading-edge voltage, this represents 400J of storedenergy. The transchest elements are estimated at: 82% current throughthe thoracic cage; 14% through the chest wall and lungs in parallel; and4% of applied current through the lung in series with the heart. Thenthe membrane resistance coefficient Ω_(M)=5.9, and the system resistancecoefficient Ω_(S)=2.3. Then the table below illustrates the applicationof the design rule as the overall chest resistance ranges from 25Ω to200Ω:

R (Ω) τ₁ d(φ₁) V_(final) E_(delivered) 25 5.2 5.05 757 343 50 10.2 6.901017 297 75 15.2 8.15 1170 263 100 20.2 9.10 1275 238 125 25.2 9.90 1350216 150 30.2 10.55 1410 201 175 35.2 11.15 1457 186 200 40.2 11.65 1497176

It should be noted and understood that the design of φ₂ is independentfrom φ₁. To design φ₂, the only information necessary from φ₁ is wherethe cell response was left when φ₁ was truncated. Additionally, φ₂ neednot use the same or similar circuitry as that used for φ₁. For example,φ may use circuitry as illustrated in FIG. 4 where φ₂ may use circuitryillustrated in FIG. 5a, or vice-versa. The corresponding design rulesfor a φ₁ circuitry may be used in conjunction with the design rules fora φ₂ circuitry, regardless of the specific circuitry used to implementeach phase of a monophasic or biphasic shock pulse.

Present Invention

The present invention is based on the charge burping model hypothesiswhich postulates and defines an optimal pulse duration for φ₂ as aduration that removes as much of the φ₁ residual charge from the cell aspossible. Ideally, the objective is to maintain unstimulated cells withno charge or set them back to relative ground.

A further objective of the present invention is to formulate ameasurement by which the optimal duration of τ_(s) (cell time constant)and τ_(m) (membrane time constant) can be measured. Although one canchoose a proper φ₂ (fixed) for a given cell response φ₁, intransthoracic shock pulse applications, τ_(m) is not known and it variesacross patients, waveforms and time. For a fixed φ₂, therefore, theerror in τ_(m) could be substantial. Realizing this, the presentinvention is designed to correct for “range” of candidate τ_(m) valuesto fit an optimal duration for a fixed φ₂. In other words, φ₂ isselected so that the capacitance in the model is matched with measuredR_(H) to get a “soft landing” to thereby minimize error due to τ_(m)±Ein charge burping ability of φ₂ involving patient variability.

The technique of “soft landing” advanced by the present invention limitsthe error in τ_(m) and sets φ₂ to dynamically adjust within a range ofpossible τ_(m) values. As discussed hereinbelow, optimizing solutionsare used to determine parameters on which intelligent calculations couldbe made so that autonomous φ₂ adjustments for variable R_(H) arepossible.

The charge burping model also accounts for removing the residual chargeat the end of φ₁ based on φ₂ delivered by a separate set of capacitorsother than those used to deliver φ₁. Referring now to FIG. 3, C₁represents the φ₁ capacitor set and C₂ represents the φ₂ capacitor,R_(H) represents the resistance of the heart, and the pair C_(m) andR_(m) represent the membrane series capacitance and resistance of asingle cell. The node V_(s) represents the voltage between theelectrodes, while V_(m) denotes the voltage across the cell membrane.

Accordingly, one of the advantages that AEDs have over ICDs, is that theimplementation of a φ₂ waveform may be completely independent of theimplementation of φ₁. Specifically, the charging and dischargingcircuits for φ₁ and φ₂ do not need to be the same circuitry. UnlikeICDs, AEDs are not strictly constrained by space and volumerequirements. Within practical limits, in AEDs the capacitance andvoltage which characterize φ₂ need not depend on the circuitry and thevalues of φ₁.

The Lerman-Deale model for AED's define the main series for current topass through the chest wall, the lungs and the heart. Further, twoshunting pathways in parallel with current pathway through the heart aredefined. Another shunting pathway is provided by the thoracic cage.However, when compared to the resistivity of the lungs, the thoraciccage resistance is rather negligible.

Thus, considering the transthoracic defibrillation model of FIG. 4,there are several other resistances in addition to those discussed forthe charge burping model hereinabove. R_(s) represents the resistance ofthe defibrillation system, including the resistance of the electrodes.R_(CW) and R_(LS) represent the resistances of the chest wall and thelungs, respectively, in series with resistance of the heart, R_(H).R_(TC) and R_(LP) represent the resistances of the thoracic cage and thelungs, respectively, in parallel with the resistance of the heart.

As discussed hereinabove, developing design equations which enableadjustments for variable resistances encountered in the transthoracicdefibrillation model of FIG. 4 is one of the advances of the presentinvention. In order to adjust for variable R_(H) both φ₁ and φ₂ areassumed fixed. Then φ₂ is selected to have a range of capacitance valueswhich permit to optimize the slope of the voltage curve at time t. Inother words, C_(S2) for φ₂ is chosen such that $\frac{v}{t} = 0$

The design parameters of the present invention are derived from equation35, as follows:

V _(M)(t)=V _(O)(1−e ⁻ ^(t/τ) ^(_(M)) ).   (35)

Equation 35 can be rewritten as: $\begin{matrix}{{{V_{M2}(t)} = {{{\left( {V_{\varphi 1} + {\left\{ \frac{\tau_{2}}{\tau_{2} - \tau_{M}} \right\} V_{2}}} \right)e\quad \frac{- \tau}{\tau_{M}}} - {\left( \frac{\tau_{2}}{\tau_{2} - \tau_{M}} \right)V_{2}^{{- t}/\tau_{2}}}} = 0.}}{{{{Letting}\quad A} = {{{V\quad \varphi_{1}} + {B\quad {and}\quad B}} = {\frac{\tau_{2}}{\tau_{2} - \tau_{M}}V_{2}}}},}} & (36)\end{matrix}$

equation 36 can be written as: $\begin{matrix}{{V(t)} = {{{Ae}\frac{- t}{\tau_{M}}} - {{Be}\quad {\frac{- t}{\tau_{2}}.}}}} & (37)\end{matrix}$

Differentiating equation 37 with respect to t, we have the following:$\begin{matrix}{\frac{v}{t} = {{{- \frac{A\quad ^{{- t}/\tau_{M}}}{\tau_{M}}} + {\frac{B}{\tau_{2}}^{{- t}/\tau_{2}}}} = 0.}} & (38)\end{matrix}$

Equation 38 is the profile of φ₁ waveform and at ${\frac{v}{t} = 0},$

the slope of the curve is zero, which means the terminal value of thetime constant is determinable at this point.

Thus, solving equation 38 for the value of t, we have: $\begin{matrix}{{t = {\frac{t_{2}}{\tau_{2} - \tau_{M}}{\tau_{M} \cdot \ln}\left\{ {\frac{\tau_{2}}{\tau_{M}}\frac{\left( {V_{\varphi 1} + {\frac{\tau_{2}}{\tau_{2} - \tau_{M}}V_{2}}} \right)}{\left( \frac{\tau_{2}}{\tau_{2} - \tau_{M}} \right)V_{2}}} \right\}}}{where}} & (39) \\{t_{1} = {\left( \frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}} \right)\quad \ln \quad \left\{ {1 + {\left( \frac{\tau_{2} - \tau_{M}}{\tau_{2}} \right)\quad \left( \frac{V_{\varphi 1}}{V_{2}} \right)}} \right\}}} & (40) \\{t_{1} = {t_{1} + {\left( {\frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}}\ln \quad \left\{ \frac{\tau_{2}}{\tau_{M}} \right\}} \right).}}} & (41)\end{matrix}$

For biphasic defibrillation waveforms, it is generally accepted that theratio of φ₁, duration (τ_(m)) to φ₂ duration (τ₂) should be ≧1. Chargeburping theory postulates that the beneficial effects of φ₂ are maximalwhen it completely removes the charge deposited on myocardial cell byφ₁. This theory predicts that φ₁/φ₂ should be >1 when τ_(s) is >3 ms and<1 when τ_(s) <3 ms. τ_(s) is defined as the product of the pathwayresistance and capacitance. (See NASPE ABSTRACTS, Section 361 entitledCharge Burping Predicts Optimal Ratios of Phase Duration for BiphasicDefibrillation, by Charles D. Swerdlow, M.D., Wei Fan, M.D., James E.Brewer, M.S., Cedar-Sinai Medical Center, Los Angeles, Calif.

In light of the proposed duration ratio of φ₁ and φ₂, wherein theoptimal solution is indicated to be at t₁=t₂ where t is the duration ofφ₁ and t₂ is the duration of φ₂ and superimposing this condition onequation 41 hereinabove, we have: $\begin{matrix}{{t_{2} = {{t_{1} + {\left( {{\frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}} \cdot \ln}\quad \left\{ \frac{\tau_{2}}{\tau_{M}} \right\}} \right)\quad {setting}\quad t_{2}}} = t_{1}}},\text{remanaging terms we have:}} & (42) \\{{{t_{2} - t_{1}} = {0 = {{\frac{\tau_{2}\tau_{M}}{\tau_{2} - \tau_{M}} \cdot \quad \ln}\quad \left\{ \frac{\tau_{2}}{\tau_{M}} \right\}}}}{or}{{\tau_{2}{\tau_{M} \cdot \ln}\quad \left( \frac{\tau_{2}}{\tau_{M}} \right)} = 0}{or}{{\ln \quad \frac{\tau_{2}}{\tau_{M}}} = 0}{or}{\frac{\tau_{2}}{\tau_{M}} = 1.}} & \quad\end{matrix}$

From the result of equation 42 we make the final conclusion that theoptimal charge burping is obtained when τ₂=τ_(m). From prior definition,we have established that τ_(m)=R_(H)·C_(S). Thus, in accordance withequation 42, τ₂=τ_(m)=R_(H)·C_(S).

Referring now to FIG. 6, a biphasic defibrillation waveform generatedusing the equations 35-42 is shown. At V_(m)=0 and dV_(m)/dt=0, φ₁ andφ₂ are equal to zero.

FIG. 7 is a schematic of a circuit which enables the implementation ofthe theory developed in the present invention. The circuit shows aplurality of double throw switches connecting a plurality of capacitors.The capacitors and the switches are connected to a charge or potentialsource. The voltage is discharged via electrodes. One aspect ofimplementing the “soft landing” charge burping technique developed inthe present invention is to fix C_(S) for φ₁ and fix C_(S) for φ₂.Further, τ_(m) is fixed. Then a range of resistance values representingR_(H) are selected. The τ_(m) and R_(H) ranges represent the patientvariability problem. The objective is to enable corrective action suchthat C_(S) values could range between 40 mf-200 mf and dv/dt=0 for τ₂.As indicated hereinabove the error in changing burping is minimized forτ₂ when dv/dt=0.

The implementation of the present invention requires that capacitor bankvalues be determined for φ₁ and φ₂. Specifically, the capacitor valuesfor φ₁ should be designed to realize dv/dt=0 and V=0 for φ₂ to minimizecharge burping error due to R_(H) and τ_(m). Where a variable resistoris used to set R_(H) thus providing a known but variable value and τ_(m)can be set within these practical ranges.

FIG. 8 depicts a biphasic defibrillation waveform 300, generated usingequations 35-42 above, in relation to a predicted patient's cellularresponse curve 304; the cellular response, as explained earlier is basedon a patient's measured impedance. As shown, the residual charge left onthe cardiac cells after delivery of φ₁ has been brought back to zerocharge, i.e. charge balanced, after the delivery of φ₂. This chargebalance has been achieved because the energy delivered has been allowedto vary.

Traditionally, all defibrillation waveforms have delivered a fixedenergy. This has been primarily because therapy has been measured injoules. These fixed energy waveforms, which include monophasic dampedsine, biphasic truncated exponential, and monophasic truncatedexponential waveforms, only passively responded to patient and/or systemimpedance.

This passive response was by charging a capacitor to a fixed voltage,wherein the voltage was adjusted depending on amount of fixed energy tobe delivered that was desired, and discharging it across the patient,whom acts as the load. The energy delivered is controlled by the simpleequation: $\begin{matrix}{E = {\frac{1}{2}{CV}^{2}}} & (43)\end{matrix}$

where: E is the energy, C is the capacitance of the charging capacitor,and V is the voltage. In the case of the truncated exponential waveform,equation 43 is extended to: $\begin{matrix}{E = {\frac{1}{2}{C\left( {V_{i}^{2} - V_{f}^{2}} \right)}}} & (44)\end{matrix}$

where: V_(i) is the initial voltage and V_(f) is the final voltage.Significantly, no form of patient impedance or system impedance appearsin either of the above equations.

With respect to system impedance, the above equations make theassumption that the internal impedance of the defibrillator is 0 ohms.This is a good approximation for truncated exponential waveforms, but itis not a good approximation for damped sine waveforms. Damped sinewaveforms typically have 10-13 ohms internal impedance. This internalimpedance effects the delivered energy. The internal impedance of thedefibrillator will absorb a portion of the stored energy in thecapacitor, thus reducing the delivered energy. For low patientimpedances, the absorbed energy can become quite significant, with onthe order of 40% of the stored energy being absorbed by the internalresistances.

With respect to patient impedance, the patient acts as the load and, assuch, the peak current is simply a function of the peak voltage viaOhm's law: $\begin{matrix}{I = \frac{V}{R}} & (45)\end{matrix}$

where: I is the current and R represents the patient's impedance. Asequation 45 indicates, the current is inversely proportional to theimpedance. This means that there is lower current flow for highimpedance patients which, in turn, means that it takes longer to deliverthe energy to a high impedance patient. This fact is further exemplifiedwhen considering the equation for a truncated exponential voltage at anypoint in time: $\begin{matrix}{{V(t)} = {\frac{1}{2}{CV}_{i}^{- \frac{t}{RC}}}} & (46)\end{matrix}$

Equation 46 shows that patient impedance, R, is reflected within in thevoltage equation which forms a part of the energy equation. Equation 46shows that the duration of a defibrillation waveform extends passivelywith impedance, since it takes longer to reach the truncate voltage.

To actively respond to system and patient impedances, as the presentinvention does with its charge burping model, the energy must be allowedto vary. To explain further, in the charge balance waveform of thepresent invention, there is a desire to exactly terminate thedefibrillation waveform when the cellular response curve returns to zerocharge, see again FIG. 8 Failing to terminate the defibrillationwaveform when the cellular response curve returns to zero charge, e.g.,overshooting or undershooting the neutral condition, can promoterefibrillation.

In achieving this charge balanced waveform, as explained in detail inthe specification above: (1) the charging capacitor is charged to aspecific charge voltage, i.e., this specific charge voltage is not asystem variable; (2) the current is controlled by the patient impedance$\left( {I = \frac{V}{R}} \right),$

i.e., the current is not a system variable; and (3) the duration of thedefibrillation pulse is controlled by the expected cellular responsecurve, i.e., duration is not a system variable. Because items 1-3 arenot system variables but rather are preset or set in accordance to thepatient at hand, the energy must be allowed to vary or thedefibrillation system is over constrained and charge balancing cannot beachieved over the range of patient impedances. To deliver fixed energyin a charge balanced system would require the ability to vary the chargevoltage. Varying the charge voltage is typically not done since thisrequires knowing the exact impedance in advance of the shock delivery.Many defibrillators measure the impedance during a high voltage chargedelivery since this is more accurate than low voltage measurements doneprior to shock delivery. Varying charge voltage also requires a moreexpensive defibrillation circuitry since capacitor costs increasedramatically with voltage.

It should be noted that due to the characteristics of the cellularresponse curve, the duration of the defibrillation pulse does increaseslightly for increases in patient impedance. This increased duration isof a much lesser effect than in a traditional truncated waveform.

Although the present invention has been described with reference topreferred embodiments, workers skilled in the art will recognize thatchanges may be made in form and detail without departing from the spiritor scope of the present invention.

What is claimed:
 1. A method for determining the second phase of abiphasic defibrillation shock pulse, said second phase having variableenergy, wherein upon application of said second phase of said biphasicdefibrillation shock pulse a desired response is produced in a patient'scardiac cell membrane, comprising: providing a quantitative model of adefibrillator circuit for producing said biphasic defibrillation shockpulse; providing a quantitative model of a patient that includes avariable heart component; providing a quantitative description of apredetermined response of said cardiac cell membrane to said shockpulse; determining a quantitative description of a first phase of saidbiphasic defibrillation shock pulse that will produce said predeterminedresponse of said cardiac cell membrane, wherein the determination ismade as a function of said predetermined response of said cardiac cellmembrane, said quantitative model of a defibrillator circuit, and saidquantitative model of a patient; and determining a quantitativedescription of a second phase of said biphasic defibrillation shockpulse based on said first phase, wherein said quantitative descriptionprovides for setting a time duration for said second phase based on saidvariable heart component whereby an amount of energy to be delivered bysaid second phase varies according to said time duration that is set. 2.The method of claim 1, wherein said predetermined response has a firstinstance of zero charge and a second instance of zero charge, andwherein said quantitative description of said first phase provides forinitiating said first phase at a time of said first instance of zerocharge and said quantitative description of said second phase providesfor setting said time duration to end at a time of said second instanceof zero charge.
 3. The method of claim 1, wherein said quantitativemodel of a patient further includes a chest component, and a cardiaccell membrane component.
 4. The method of claim 1, wherein the step ofproviding a quantitative model of a patient is carried out with acircuit having at least one defibrillation system resistance component.5. The method of claim 1, wherein the step of providing a quantitativemodel of a patient is carried out with a circuit having at least onechest wall resistance component.
 6. The method of claim 1, wherein thestep of providing a quantitative model of a patient is carried out witha circuit having a thoracic cage resistance component.
 7. The method ofclaim 1, wherein the step of providing a quantitative model of a patientis carried out with a circuit having a one lung series resistancecomponent.
 8. The method of claim 1, wherein the step of providing aquantitative model of a patient is carried out with a circuit having aone lung parallel resistance.
 9. The method of claim 1, wherein the stepof providing a quantitative model of a patient is carried out with acircuit having a chest wall resistance component, a thoracic cageresistance component, and a lung resistance component.
 10. The method ofclaim 1, wherein the step of providing a quantitative model of a patientis carried out with a circuit having a lung parallel resistancecomponent connected in parallel with said variable heart component. 11.The method of claim 1, wherein the step of providing a quantitativemodel of a patient is carried out with a circuit having a thoracic cageresistance component connected in parallel with said variable heartcomponent.
 12. The method of claim 1, wherein the step of providing aquantitative model of a defibrillator circuit is carried out with acircuit having first and second capacitors.
 13. The method of claim 1,wherein the step of providing a quantitative model of a patient iscarried out with a circuit having a lung parallel resistance componentand a thoracic cage resistance component connected in parallel with saidvariable heart component.
 14. A defibrillation apparatus for deliveringa biphasic defibrillation shock pulse to produce a desired response in apatient's cardiac cell membrane, wherein a second phase of said biphasicdefibrillation shock pulse has a variable energy, comprising: adefibrillator circuit; and a pair of electrodes operably coupled to saiddefibrillator circuit, wherein said pair of electrodes delivers saidbiphasic defibrillation shock pulse to said patient's cardiac cellmembrane, wherein said defibrillator circuit has been configuredaccording to: a quantitative model of a defibrillator circuit forproducing said biphasic defibrillation shock pulse; a quantitative modelof a patient that includes a variable heart component; and aquantitative description of a predetermined response of said cardiaccell membrane to said shock pulse; a quantitative description of a firstphase of said biphasic defibrillation shock pulse that will produce saidpredetermined response of said cardiac cell membrane, wherein saidquantitative description of said first phase has been determined fromsaid predetermined response of said cardiac cell membrane, saidquantitative model of said defibrillator circuit, and said quantitativemodel of said patient; and a quantitative description of a second phaseof said biphasic defibrillation shock pulse wherein said quantitativedescription of said second phase has been determined based on said firstphase and wherein said quantitative description of said second phaseincludes a time duration setting that has been based on said variableheart component whereby an amount of energy to be delivered by saidsecond phase varies according to said time duration setting.
 15. Theapparatus of claim 14, wherein said predetermined response has a firstinstance of zero charge and a second instance of zero charge, andwherein said quantitative description of said first phase includesinitiating said first phase at a time of said first instance of zerocharge and said quantitative description of said second phase includessaid time duration setting that ends said second phase at a time of saidsecond instance of zero charge.
 16. The apparatus of claim 14, whereinsaid quantitative model of a patient further includes a chest componentand a cardiac cell membrane component.
 17. The apparatus of claim 14,wherein said defibrillator circuit includes a defibrillation systemresistance component.
 18. The apparatus of claim 14, wherein saiddefibrillator circuit includes a chest wall resistance component. 19.The apparatus of claim 14, wherein said defibrillator circuit includes athoracic cage resistance component.
 20. The apparatus of claim 14,wherein said defibrillator circuit has a lung series resistancecomponent.
 21. The apparatus of claim 14, wherein said defibrillatorcircuit has a lung parallel resistance component.
 22. The apparatus ofclaim 14, wherein said defibrillator circuit has a chest wall resistancecomponent, a thoracic cage resistance component, and a lung resistancecomponent.
 23. The apparatus of claim 14, wherein said defibrillatorcircuit has a lung parallel resistance component connected with parallelwith a variable heart resistance component.
 24. The apparatus of claim14, wherein said defibrillator circuit has a thoracic cage resistancecomponent connected in parallel with a variable heart resistancecomponent.
 25. The apparatus of claim 14, wherein said defibrillatorcircuit has a first and second capacitor.
 26. The apparatus of claim 14,wherein said defibrillator circuit has a lung parallel resistancecomponent and a thoracic cage resistance component connected in parallelwith a variable heart resistance component.
 27. A defibrillationapparatus for delivering a biphasic defibrillation shock pulse toproduce a desired response in a patient's cardiac cell membrane, whereina second phase of said biphasic defibrillation shock pulse has avariable energy, comprising: an electronic circuit having adefibrillator portion and a patient modeling portion; and a pair ofelectrodes operably coupled to said electronic circuit, wherein saidpair of electrodes delivers said biphasic defibrillation shock pulse tosaid patient's cardiac cell membrane, wherein said electronic circuithas been configured according to: a quantitative model of adefibrillator circuit for producing said biphasic defibrillation shockpulse; a quantitative model of a patient that includes a variable heartcomponent; and a quantitative description of a predetermined response ofsaid cardiac cell membrane to said shock pulse; a quantitativedescription of a first phase of said biphasic defibrillation shock pulsethat will produce said predetermined response of said cardiac cellmembrane, wherein said quantitative description of said first phase hasbeen determined from said predetermined response of said cardiac cellmembrane, said quantitative model of said defibrillator circuit, andsaid quantitative model of said patient; and a quantitative descriptionof a second phase of said biphasic defibrillation shock pulse whereinsaid quantitative description of said second phase has been determinedbased on said first phase and wherein said quantitative description ofsaid second phase includes a time duration setting that has been basedon said variable heart component whereby an amount of energy to bedelivered by said second phase varies according to said time durationsetting.
 28. The apparatus of claim 27, wherein said predeterminedresponse has a first instance of zero charge and a second instance ofzero charge, and wherein said quantitative description of said firstphase includes initiating said first phase at a time of said firstinstance of zero charge and said quantitative description of said secondphase includes said time duration setting that ends said second phase ata time of said second instance of zero charge.
 29. The apparatus ofclaim 27, wherein said quantitative model of a patient further includesa chest component and a cardiac cell membrane component.
 30. Theapparatus of claim 27, wherein said patient modeling portion includes adefibrillation system resistance component.
 31. The apparatus of claim27, wherein said patient modeling portion includes a chest wallresistance component.
 32. The apparatus of claim 27, wherein saidpatient modeling portion includes a thoracic cage resistance component.33. The apparatus of claim 27, wherein said patient modeling portion hasa lung series resistance component.
 34. The apparatus of claim 27,wherein said patient modeling portion has a lung parallel resistancecomponent.
 35. The apparatus of claim 27, wherein said patient modelingportion has a chest wall resistance component, a thoracic cageresistance component, and a lung resistance component.
 36. The apparatusof claim 27, wherein said patient modeling portion has a lung parallelresistance component connected with parallel with a variable heartresistance component.
 37. The apparatus of claim 27, wherein saidpatient modeling portion has a thoracic cage resistance componentconnected in parallel with a variable heart resistance component. 38.The apparatus of claim 27, wherein said defibrillator portion has afirst and second capacitor.
 39. The apparatus of claim 27, wherein saidpatient modeling portion has a lung parallel resistance component and athoracic cage resistance component connected in parallel with a variableheart resistance component.